Abstract

Hierarchical identity-based fully homomorphic encryption (HIBFHE) aggregates the advantages of both fully homomorphic encryption (FHE) and hierarchical identity-based encryption (HIBE) that permits data encrypted by HIBE to be processed homomorphically. This paper mainly constructs a new leveled HIBFHE scheme based on Learning with Rounding (\(\textsf {LWR}\)) problem, which removes Gaussian noise sampling in encryption process. In more detail, we use the lattice basis delegation method proposed by Agrawal, Boneh and Boyen at CRYPTO 2010 to generate delegated basis, while cleverly exploit a scaled rounding function of LWR problem to hide plaintext rather than adding an auxiliary Gaussian noise matrix. Besides, Gentry, Sahai and Waters constructed the first leveled LWE-based HIBFHE schemes from identity-based encryption scheme at CRYPTO 2013, in this work, however, we also focus on improving their leveled HIBFHE scheme, using Alperin-Sheriff and Peikert’s technically simpler method. We prove that our schemes are adaptively secure under classic lattice hardness assumptions.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their detailed reviews and helpful comments. This research is supported in part by the National Nature Science Foundation of China (Nos. 61672030, 61272040 and U1705264; Nos. 61572132 and U1705264).